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Simplifying y2 + 16y + -63 = 0 Reorder the terms: -63 + 16y + y2 = 0 Solving -63 + 16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 16y + 63 + y2 = 0 + 63 Reorder the terms: -63 + 63 + 16y + y2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 16y + y2 = 0 + 63 16y + y2 = 0 + 63 Combine like terms: 0 + 63 = 63 16y + y2 = 63 The y term is 16y. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16y + 64 + y2 = 63 + 64 Reorder the terms: 64 + 16y + y2 = 63 + 64 Combine like terms: 63 + 64 = 127 64 + 16y + y2 = 127 Factor a perfect square on the left side: (y + 8)(y + 8) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (y + 8) equal to 11.26942767 and -11.26942767.Subproblem 1
y + 8 = 11.26942767 Simplifying y + 8 = 11.26942767 Reorder the terms: 8 + y = 11.26942767 Solving 8 + y = 11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + y = 11.26942767 + -8 y = 11.26942767 + -8 Combine like terms: 11.26942767 + -8 = 3.26942767 y = 3.26942767 Simplifying y = 3.26942767Subproblem 2
y + 8 = -11.26942767 Simplifying y + 8 = -11.26942767 Reorder the terms: 8 + y = -11.26942767 Solving 8 + y = -11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -11.26942767 + -8 Combine like terms: 8 + -8 = 0 0 + y = -11.26942767 + -8 y = -11.26942767 + -8 Combine like terms: -11.26942767 + -8 = -19.26942767 y = -19.26942767 Simplifying y = -19.26942767Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.26942767, -19.26942767}
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